单位球中的极小曲面

Minimal Surfaces in a Unit Sphere

中文关键词:  小曲面  高斯曲率  法数量曲率.

英文关键词:minimal surface  Gauss curvature  normal scalar curvature.

中文摘要:

      令$M$是浸入到单位球$S^{n}$中具有正高斯曲率的极小曲面.我们在曲面$M$上选取一组单位正交标架场,在这组标架场下,形状算子具有很简便的形式.我们也给出了这组标架场的一些应用.

英文摘要:

      Let $M$ be a closed surface with positive Gauss curvature minimally immersed in a standard Euclidean unit sphere $S^{n}$. In this paper, we choose a local orthonormal frame field on $M$, under which the shape operators have very convenient form. We also give some applications of this kind of frame field.